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Sig Fig rules handout and exact numbers

To determine the number of significant
figures in a number, we follow these rules:
1. All nonzero digits are significant.
2. Interior zeros (zeros between two numbers) are significant.
3. Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal
point are significant.
4. Trailing zeros that fall before a decimal point are significant.
5. Leading zeros (zeros to the left of the first nonzero number) are not significant.
They only serve to locate the decimal point.
o For example, the number 0.0005 has only one significant digit.
6. Trailing zeros at the end of a number, but before an implied decimal point, are
ambiguous and should be avoided by using scientific notation.
o For example, it is unclear if the number 350 has two or three significant
figures. We can avoid confusion by writing the number
as 3.5×1023.5×102 to indicate two significant figures or
as 3.50×1023.50×102 to indicate three.
Exact Numbers
Exact numbers have an unlimited number of significant figures. Exact numbers
originate from three sources:
Exact counting of discrete objects. For example, 10 pencils means 10.0000 . . .
pencils and 3 atoms means 3.00000 . . . atoms.
Defined quantities, such as the number of centimeters in 1 m. Because 100 cm is
defined as 1 m then can be defined as:
100 cm=1 m means 100.00000... cm=1.0000000... m
Note that some conversion factors (see Section 2.6) are defined quantities while others
are not.
Integral numbers that are part of an equation. For example, in the equation,
The number 2 is exact and therefore has an unlimited number of significant figures.